Frames and Slicings for Angular Momentum in Post-Minkowski Scattering

TL;DR

This paper explores how different choices of time slicing and asymptotic frames in relativistic scattering affect angular momentum and mass moments, proposing a flux balance law in post-Minkowski theory.

Contribution

It introduces a framework using hyperboloidal slices and BMS transformations to reconcile angular momentum calculations in scattering, extending to all orders in post-Minkowski expansion.

Findings

Using hyperboloidal slices aligns mass moment calculations.

BMS transformations relate early and late time frames.

Conjecture of a comprehensive flux balance law in post-Minkowski theory.

Abstract

In relativistic physics, angular momentum is paired with a lesser known conserved quantity, the "mass moment", which appears as the time-space components of the angular momentum tensor. Calculations of mass moment in electromagnetic and gravitational scattering of point particles have led to some puzzling behavior in which the radiated mass moment does not appear to match the corresponding mechanical change. We review the issues and show how the freedoms of time slicing and asymptotic frame may be used to bring all known results into agreement. The key points are to use hyperboloidal time slices and to allow the perturbative and asymptotic frames to differ by an independent Bondi-Metzner-Sachs (BMS) transformation at early and late times. The relevant BMS transformation involves a translation found recently by Riva, Vernizzi, and Wong. Building on this work, we conjecture a flux balance law for all orders in the post-Minkowski expansion.